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The next generation

27 November 2012

A team from Georgia Institute of Technology, the University of Michigan and Prairie View A&M University have proposed a current-mode implementation of a ‘zigzag’ chaotic map that is low-power, high speed and robust to process variations, allowing truly random number generation with fairly simple post-processing of the generated bits.

A security matter

A truly random number generator (TRNG) is a device that generates an ‘unbiased’ and ‘independent’ binary stream and is an essential component in applications such as public key cryptography and digital signature schemes.

With secure data processing such as banking and emails increasingly being used on small mobile devices, there is a growing demand for high-speed embedded TRNGs to ensure the security of the data transmission at the hardware level.

One of the best solutions for high speed TRNG is based on discrete-time chaos maps. This works by the amplification of the inherent noise of the analogue circuitry in a chaotic map function: the output of the map is fed back into the map as the input at defined time steps which leads to the amplification of the noise and creates unpredictable output behaviour. The state of the map output at each time step is transformed into a binary random variable using a bit generation function. The discrete-time nature of the circuit makes chaotic map TRNGs much faster than other methods such as oscillator-based TRNGs and they are also easier to embed into integrated circuits.

Back to reality

A problem with chaotic-map TRNGs is that, in a real implementation, they suffer from saturation of the output in the corner points of the map. This is due to process variations which impact on the map function, causing the output to be trapped in either all-zero or all-one state. To overcome this some researchers have proposed the use of sub-optimal maps that solve the saturation problem of the corner points but compromise the truly randomness of the generated bits.

The alternative solution presented by the US-based team in this issue of Electronics Letters uses a zigzag map in which the output alternates between positive and negative values to overcome the corner point saturation problem. It is also a ‘continuous’ mapping, and this continuity enables a simple current-mode implementation that is low-power and high speed.

The current-mode implementation also has the big advantage of being more robust to process variations. These variations translate as a shift in the bit threshold or changes in the slope of the map function, and affect the correlation of the bits output binary sequence. Post-processing is therefore needed to improve the degraded performance and generate truly random bits from the map. The current-mode implementation of the zigzag map is much more robust and needs only fairly simple post-processing of the bits which reduces the complexity and cost of the post-processing unit.

Future optimisation

This work is now continuing as part of the collective effort between Georgia Institute of Technology, the University of Michigan and Prairie View A&M University.

“Our efforts target the design of more efficient TRNGs and post-processing algorithms that are very close to the fundamental performance limits of truly random number generators,” said Ahmad Beirami from Georgia Tech.

“Our expertise (as a team) in a broad range of research areas, such as information theory, analogue and digital circuit design, circuit optimisation, and hardware implementation has enabled our rapid research advancement,” added Beirami.

“We do not see ourselves confined to just solving one problem and one application. We are also persistently targeting challenging research problems that require multi-disciplinary expertise for a novel and efficient solution, such as the modelling and optimisation of nano-photonic devices and the design of efficient compressive sensing ADCs,” said Hamid Nejati from University of Michigan.

“The ever-increasing volume of data transmission, and in particular mobile data, requires high speed embedded TRNGs for several applications. As different applications have various requirements on the randomness, speed, power, and size of the TRNG, there is not a single solution that meets all of these requirements. Thus, we expect the future work (by us or other researchers) to explore these trade-offs and offer optimised solutions for various applications,” added Nejati.